A. Field of the Invention
This invention relates to a method based on future economic factors for determining when a drill bit that is being used in drilling operations should be replaced. The principal application for the present method is in drilling for hydrocarbons both onshore and offshore; however, the present method is applicable to any type of drilling, mining, or manufacturing operation that requires the periodic replacement of a bit or tool.
The cost of drilling a well is a function of the rate at which the well can be drilled which, in turn, depends on the penetration rate of each drill bit, a unit of measure that quantifies the rate at which the bit enters the subsurface formation. In general, the penetration rate, in feet per hour, decreases over the life of the bit as it wears. (See FIG. 1). This decrease in the penetration rate and the resulting increase in the expected unit cost necessitates an eventual decision by drilling or engineering personnel to replace the bit.
The bit replacement decision is important in economic terms because higher drilling costs will result if the bit is pulled too soon or if it is left in the borehole too long. The present method ensures that the bit replacement decision is made at the optimal point that minimizes expected controllable unit drilling costs.
The bit replacement process requires a "trip", an operation in which the drill string, consisting of drill pipe, drill collars, stabilizers, and the drill bit, is pulled out of the hole. The bit has to be replaced, and the entire assembly must be lowered back into the hole before drilling can commence.
On most drilling rigs, the bit replacement decision is made on the basis of subjective estimates of the extent of bit wear, i.e., a bit that is "worn out" should be replaced. In certain cases, consideration is given to the economics of bit replacement; however, previous techniques used to quantify the replacement decision are not correct. Th present method, by contrast, directly compares the current bit and a replacement bit on the basis of the total expected controllable unit cost over a future drilling interval. (See FIG. 2).
The comparison of the current bit with a replacement bit depends on an accurate, predictive penetration rate model. The penetration rate model given in this invention is a multivariate model consisting of drilling variables that are known to have a significant effect on the penetration rate of a bit under real-time conditions.
In the normal operating mode, the present method is concerned with the question of bit replacement as opposed to bit selection. The decision generated by the present method is based on data collected on the current bit and thus in the normal operating mode applies to a replacement bit of the same design.
The methodology described in this invention utilizes a predictive variance statistic which ensures that the penetration rate model is based on the best available predictor variables. With this statistic, variables that may be quantified through future technological advances may be evaluated for inclusion in the penetration rate model.
The invention also describes an expression for calculating the total expected controllable unit cost which allocates bits costs, rig operating costs, and tripping costs over a future drilling interval.
B. Description of the Prior Art
The most common method of determining when a drill bit should be changed is based on the experience of on-site drilling personnel who make subjective decisions regarding the condition of the bit. When the bit is judged to be either completely or extensively worn, it is replaced. This method minimizes one cost component, the cost of the bit, while disregarding the operating cost of the rig which, in many cases, is a more significant cost. Consequently, it is only a matter of coincidence if bit changes based on complete wear of the bit also result in the minimum expected unit cost.
On occasion, a drill bit change schedule is formulated prior to the actual drilling of the well. This method, referred to herein as the "correlation approach", is based on examining the drilling records of wells that were drilled in the same general region of the proposed well and reflects the subjective approach to estimating bit wear previously described. In this method, a drilling engineer attempts to correlate the penetration rate of the drill bits with the lithology of the wells in which they were used. By assuming that the lithology of the proposed well will be virtually identical to other wells in the same area and by assuming that the bit should be changed when it is "worn out", the drilling engineer formulates a bit change schedule for the proposed well based upon the bit changes that occurred in adjacent wells. The correlation approach to the bit replacement decision is inadequate if the objective is to minimize the expected controllable unit cost of the well. However, the correlation method may correctly be used for bit selection purposes, i.e., to decide what type bit should be ueed in different zones of the well.
Yet another bit replacement method attempts to quantify the decision by determining the historical cost per foot of the bit presently in the hole and comparing this value to some proprietary threshold value of cost per foot previously established by the drilling company or its client. As it is used herein, the term "historical cost per foot" refers to unit costs determined by allocating all previous bit, tripping and operating costs over the actual interval drilled with the current bit. There are several shortcomings associated with this method including the following: (1) only historical costs attributed to the current bit are calculated, i.e., the expected unit costs of the current bit are not directly compared with the expected unit costs of a replacement bit, (2) it does not differentiate between costs that are properly allocated to the current bit versus those that should be allocated to a replacement bit, and (3) a corporate threshold value of cost per foot is based on costs incurred in other wells and may have no relevance to the hole being drilled.
In a variation of this technique, the instantaneous penetration rate (or some approximation thereof such as the rate computed over an interval of five or ten feet) is compared to a proprietary company value of penetration rate based on some threshold cost per foot value. When the instantaneous penetration rate falls below the company threshold value, bit replacement is recommended.
U.S. Pat. No. 3,752,966 of Foy, Jr. and Chang is based on the assumption that the bit should be changed when the historical cost per foot begins to increase. This method assumes that the historical cost per foot decreases as bit and tripping costs are prorated over an increasing interval of footage drilled. However, when the bit begins to wear significantly, the increasing marginal cost per foot that results from a decreasing penetration rate has a greater effect on the historical cost per foot and causes it to rise. According to Foy, Jr. and Chang, if the most recently calculated cost per foot exceeds the prior value, bit replacement is recommended.
There is no assurance that the method of Foy, Jr. and Chang minimizes the expected cost per foot since only two historical cost values of the current bit are being compared. The current bit is not directly compared to a replacement bit nor does the method reflect future penetration rate patterns or the expected cost per foot arising thereof. Additional problems may arise if this method is used without regard to projected aasing setting depths or logging intervals since an unnecessary trip to change the bit might occur within a short interval of a nondiscretionary trip.